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2 years ago

11

An experiment consists of randomly selecting a card from a box containing cards numbered 1-12. Which has the smallest probabilit

y?
F. P(greater than 8)
G. P(multiple of 4)
H. P(even number)
J. P(less than 5)

1 answer:

deff fn [24]2 years ago

3 0

G. P(multiple of 4) is the answer

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17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find

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Answer:

$r = 3.74cm$

Step-by-step explanation:

Given

Hemisphere

$Radius = 7cm$

Cone

$Height = 49m$

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

$V_1 = \frac{2}{3}\pi r^3$

Substitute 7 for r

$V_1 = \frac{2}{3}\pi * 7^3$

$V_1 = \frac{2}{3}\pi * 343$

$V_1 = \frac{686}{3}\pi$

Volume (V2) of a cone is:

$V_2 = \frac{1}{3}\pi r^2h$

Because the lead is cast into a cone, then they have the same volume.

So, we have:

$\frac{686}{3}\pi = \frac{1}{3}\pi r^2h$

$686 = r^2h$

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$686 = r^2 * 49$

Divide both sides by 49

$r^2 = \frac{686}{49}$

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$r = \sqrt{14$

$r = 3.74cm$

<em>Hence, the radius of the cone is 3.74cm</em>

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